Physics-informed neural networks for the modelling of interferometer-polarimetry in tokamak multi-diagnostic equilibrium reconstructions

Equilibrium reconstruction is crucial in nuclear fusion and plasma physics, as it enables the understanding of the distribution of fundamental plasma quantities within a reactor. Given that equilibrium reconstruction is an ill-posed problem, it is essential to constrain the algorithm with multiple diagnostics to achieve accurate results. Among these, the interferometer-polarimeter is one of the most valuable diagnostics for constraining equilibrium reconstruction, as it provides line-integrated information about the internal magnetic fields. However, the polarisation evolution of an electromagnetic wave traversing a magnetised plasma exhibits non-linear behaviour, making it challenging to incorporate polarimeter data into the reconstruction process. This difficulty often leads to the use of a linear approximation, known as the type-I approximation, in the inversion algorithm. Unfortunately, this approximation can significantly limit the accuracy of the reconstructions in many cases. In this work, we present a physics-informed neural network (PINN) algorithm for reconstructing plasma equilibrium using a multi-diagnostic approach that includes magnetics, Thomson scattering, and interferometer-polarimeter data. The PINN algorithm employs three models for reconstruction: the first uses the type-I approximation, the second uses the non-linear polarization equation under the cold-plasma approximation, and the third uses a comprehensive model that accounts for thermal effects, both relativistic and non-relativistic (defined as the hot plasma model). Parametric analyses conducted on synthetic cases demonstrate that the hot plasma model consistently yields the best results, while reconstructions using the type-I or cold plasma approximations are prone to systematic errors in the reconstructed plasma quantities. The PINN model has been tested on ITER-like plasma configurations with noisy measurements, showing that the inclusion of interferometer-polarimeter data significantly improves accuracy, achieving around 99.9%. Future work aims to transfer the algorithm to existing experimental nuclear fusion reactors and to integrate additional diagnostics for further enhancing the reliability and accuracy of the solutions.